arXiv subjects

Pierre A Mandrin

Publications and source records attributed to Pierre A Mandrin.

3 recordsLinked to original sources

arXiv2025

Statistical mechanical space-time decomposition as a key to a (non-perturbative) quantization prescription for gravity

By assuming gravity and matter to be subject to a joint statistical mechanical concept (JSMC) and interpreting Rindler horizon sections as open thermodynamic systems, one arrives at a specific new form of non-perturbative Lorentzian path integral quantisation in a compact space-time region, with well-determined gravitational measure, adequate fixing of boundary conditions and causal geometries. JSMC implies a space-time decomposition, leading to a sum over configurations in line with path integral methods. In these developments, we carefully distinguish the concepts of Boltzmann's statistical mechanics and the path integral.

physics.gen-ph↗

arXiv2025

What quantum matter tells about quantisation of gravity in a statistical mechanics context

We propose a "guide" towards quantisation of gravity based on quantum matter in a statistical mechanics context. On one hand, a statistical mechanics model naturally arises from the thermodynamic interpretation of horizons in Rindler space. On the other hand, the path integral formulation of quantum field theory can be interpreted from the point of view of statistical mechanics. From these perspectives, gravity and matter are related to each other in the same way as a gas and its chemical potential are. This statistical mechanics interpretation of gravity and matter suggests that gravity should be quantised in a precise way which is determined by the quantisation of matter. Although, in a first step, quantisation of gravity applies for small perturbations of the metric with respect to the vacuum, the most central and general features of quantisation (quantisation prescription, quantum space dimensions) are supported from statistical mechanics and remain valid non-perturbatively.

gr-qc↗

arXiv2018

Multi-layer statistical gravity on the boundary

Starting from an important research path, we consider gravity as a collective phenomenon governed by statistical mechanics. While previous studies have focussed on the thermodynamic heat flow across a 2d-horizon as perceived by a single, accelerated observer, we evaluate here the number of microscopic states arising for multiple observers perceiving multiple horizons within foliations of the boundary of a space-time region. This yields a temperature-independent, Boltzmann-type "entropy" which is equivalent to the boundary action and which we call m-entropy. According to its statistical interpretation, the m-entropy distribution as a function of the gravitational field is maximum when Einstein's Field Equations hold. However, if the number of "atoms of space" is small, Einstein's Equations do not hold and no sharp geometry can be defined. On the other hand, the transition probability of microstates can be computed and can be interpreted as processes of a (alternative) model of quantum space-time.

gr-qc↗